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201.
Vern I. Paulsen Dinesh Singh 《Proceedings of the American Mathematical Society》2001,129(4):1097-1103
This paper presents a generalization of the invariant subspace theorem of Helson and Lowdenslager along the lines of de Branges' generalization of Beurling's theorem.
202.
Holger Dette 《Proceedings of the American Mathematical Society》2001,129(6):1805-1815
For a birth and death chain on the nonnegative integers, integral representations for first return probabilities are derived. While the integral representations for ordinary transition probabilities given by Karlin and McGregor (1959) involve a system of random walk polynomials and the corresponding measure of orthogonality, the formulas for the first return probabilities are based on the corresponding systems of associated orthogonal polynomials. Moreover, while the moments of the measure corresponding to the random walk polynomials give the ordinary return probabilities to the origin, the moments of the measure corresponding to the associated polynomials give the first return probabilities to the origin.
As a by-product we obtain a new characterization in terms of canonical moments for the measure of orthogonality corresponding to the first associated orthogonal polynomials. The results are illustrated by several examples.
203.
Vern I. Paulsen Dinesh Singh 《Proceedings of the American Mathematical Society》2004,132(12):3577-3579
We prove a uniform algebra analogue of a classical inequality of Bohr's concerning Fourier coefficients of bounded holomorphic functions. The classical inequality follows trivially.
204.
Holger Boche 《manuscripta mathematica》1998,95(2):137-147
The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous function g
1∈C
0 [0,1]2 with support in the rectangle [0,1] × [0,?] is indicated in the paper for which the two dimensional Shannon sampling series
diverge almost everywhere in the rectangle [0,1] × [?,1]. This shows that the localization principle for Shannon sampling
series cannot hold in two dimensions and in higher dimensions. The result solves a problem formulated by P.L. Butzer.
Received: 21 December 1995 / Revised version: 5 October 1996 相似文献
205.
The present paper deals with the formulation of minimal loading conditions for the application of numerical homogenisation techniques, namely the FE2 methodology. Based on the set of volume averaging rules connecting the heterogeneous micro and the homogeneous macro scale, the minimal constraints on the deformation of a micro volume are derived for a classical Cauchy continuum as well as for a micromorphic continuum theory. For both cases, numerical studies are included highlighting the main aspects of the proposed procedure within the context of small deformations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
206.
Designs, Codes and Cryptography - We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and... 相似文献
207.
The reaction matrix of a cavity with attached waveguides connects scattering properties to properties of a corresponding closed billiard for which the waveguides are cut off by straight walls. On the one hand, this matrix is directly related to the S-matrix, on the other hand it can be expressed by a spectral sum over all eigenfunctions of the closed system. However, in the physically relevant situation where these eigenfunctions vanish on the impenetrable boundaries of the closed billiard, the spectral sum for the reaction matrix, as it was used before, fails to converge and does not reliably reproduce the scattering properties. We derive here a convergent representation of the reaction matrix in terms of eigenmodes satisfying Dirichlet boundary conditions and demonstrate its validity in the rectangular and the Sinai billiards. 相似文献
208.
Holger Lyre 《International Journal of Theoretical Physics》1995,34(8):1541-1552
The quantum theory of ur-objects proposed by C. F. von Weizsäcker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the universal symmetry groupSU(2), and can only be characterized asone bit of potential information. In this sense it is not a spatial but aninformation atom. The physical structure of the ur theory is reviewed, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy, and matter, which in ur theory appear to be directly connected with information as the fundamental substance. This hopefully will help to provide a new understanding of the concept of information. 相似文献
209.
Holger Dette 《Transactions of the American Mathematical Society》1996,348(2):691-711
A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.
210.
It is shown that the recent observations of NASA's Explorer mission, "Wilkinson Microwave Anisotropy Probe," hint that our Universe may possess a nontrivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume. 相似文献